JOINT DEVELOPMENT AND LOW- FREQUENCY INDUCTION 211 



respect to each other and to earth. To the extent that the capacitances 

 and inductances of the several phase conductors differ, residual voltages 

 and currents will result. Transpositions afford a means for compen- 

 sating for these circuit unbalances. 



In cases for which protective measures are being considered, it is 

 important to be able to estimate the magnitude of the residual current 

 when faults occur at different points on the power system. Apart from 

 inductive effects, this is a question of importance to power companies, 

 since forecast of currents under different fault conditions is essential 

 in the design and setting of protective relays. Much work has there- 

 fore been done by different investigators on methods of predetermining 

 these currents. Helpful mathematical methods have been developed, 

 though sometimes the results obtained by their use are open to question 

 due to lack of accurate values of some of the important impedances. 

 Proper allowance for fault impedance and the effect of ground wires is 

 sometimes difficult to determine and in cases of complicated networks 

 approximations usually have to be made. To facilitate the numerical 

 computations, calculating boards of varying degrees of elaborateness 

 have been developed. The subcommittee is investigating this matter 

 and by experimental work is checking the results of estimates and 

 acquiring further knowledge of the range of the variable factors. 

 Through this work, it is hoped to increase the convenience and accuracy 

 of these important computations. 



Exposure Conditions.— The relationship between power and tele- 

 phone lines with respect to the exposure conditions is defined by the 

 "coupling coefficient" or "coeffiicient of induction," a factor which, 

 when multiplied by the value of current (or voltage) in the power line, 

 gives the resulting voltage set up in the telephone line. A power line 

 and a neighboring telephone line have several different coupling 

 coefficients corresponding to different conditions, such as, whether 

 the induced voltages are due to power current or power voltage, to 

 balanced or residual components, and whether they are voltages in- 

 duced along the conductors (or to ground) or are induced directly in the 

 metallic circuit. Low-frequency induction is predominantly magnetic 

 in character and the coupling which is most significant is that between 

 the power conductors and the telephone conductors, both considered 

 with earth return. The induced voltages are due principally to 

 "longitudinal circuit induction." 



A number of dimensional factors affect the magnitude of this 

 coupling, such as the length of the exposure, the separation between 

 lines, and the locations of ground connections on the two systems. 

 Local conditions as to earth conductivity and the arrangement of 



